Question: Rewrite as a simplified fraction. ${0.57\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 574.4444...\\ 100x &= 57.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 517}$ ${x = \dfrac{517}{900}} $